A tricky and lucrative problem has existed for decades in the airline industry that was ripe for a mathematician to solve. Given a set of criteria, what is the most efficient order in which to land airplanes during inclement weather?
Many obstacles arise when inclement weather strikes an airport. One of the biggest issues is the reshuffling of airplanes that need to be landed. When this inclement weather strikes, a Ground Delay Program is run which delays some flights from landing during the inclement weather, while others may even be canceled. This effort is called a Ground Delay Program. Once a Ground Delay Program has been run, there must be a new schedule in which the flights are landed, as some can no longer make the time slot for which they were originally assigned, while others could arrive much earlier. There are, however, legal issues; you cannot just take away an airline’s landing slot at an airport without a justified trade. The issues of efficiency and legal issues complicate this algorithm, and also make it a lucrative problem to be solved.
At this point you may be familiar with matching problems, but usually these matching problems, such as the stable marriage problem, deal only with two different groups with preferences. What if, as is the case here, there is a set of criteria that needs to be satisfied on top of the preferences? How do we consider factors such as the estimated time of arrival and the property rights of the airlines when coming up with an algorithm? James Schummer and Rakesh Vohra developed an algorithm that attempts to do just that. In this presentation, we’ll see the development of the model and how graph theory was creatively used to solve this problem.